Calibration refers to the process of using empirical data and prior knowledge to determine how to estimate quantitative analyses from new measurements via some mathematical process.
Many analytical instruments provide responses that do not directly relate to desired quantitative measurements. For example, a chromatogram contains a series of peaks that relate to the amounts of components injected for analysis, but each component may have differing response factors that would bias the analysis unless a calibration were performed to determine and correct for these individual response factors.
Similarly, spectroscopic measurements such as those from infrared spectroscopy provide a vibrational spectrum that relates to the molecular motions of the individual components. Each vibrational motion has a certain response factor dependent on the characteristics of the molecule. For example, hydroxyl functionalities provide strong vibrational features, while carbon-sulfur bonds yield weak vibrational features in infrared spectra. The response factors affect the relative intensities of each vibrational band such that direct analysis of vibrational intensities will not yield accurate quantitative measurements. Calibration provides the means by which the relative response factors are accounted for in the transformation of the vibrational spectral data to quantitative measurements.
Near infrared spectrometry (NIRS) provides molecular vibrational motion data that is indirectly related to the desired quantitative measurement for many relatively complex chemical mixtures. NIRS instrumentation, data collection, and calibration are discussed in Stark et al., "Near-Infrared Analysis (NIRA): A Technology for Quantitative and Qualitative Analysis," Appl. Spec. Rev. 1986, Vol. 22, pp 335-399; Miller, "Near-Infrared Spectroscopy of Synthetic Polymers," Appl. Spec. Rev., 1991, Vol. 26, pp 227-339; and Martin, "Recent Advances in Near-Infrared Reflectance Spectroscopy," Appl. Spec. Rev., 1992, Vol. 27, pp 325-383, the disclosures of which are incorporated herein by reference. NIRS measures the absorbance of incident radiation at various wavelengths to ascertain a vibrational spectrum. The absorbance of radiation at different wavelengths indicates the presence of different vibrational motions, which in turn can be related to the desired quantitative measurements. NIRS is a highly useful technique that can provide quick and precise multivariate signal responses for on-line or in situ process environments.
Raman spectrometry is a complementary analytical technique to NIRS that also provides molecular vibrational information. Raman spectrometry measures the inelastic scattering of incident radiation from a sample and compares the inelastically scattered radiation to the incident radiation energy to provide an energy loss spectrum that relates to the vibrational motion of sampled molecules. The energy loss spectrum can be related to the desired quantitative measurements. Raman spectrometry can also provide a quick and precise multivariate signal response. Because of the contrasting nature of the scattering process in Raman compared to absorbance process in NIRS, different quantitative measurement problems can be solved by these two techniques.
There are often several interfering systematic or random effects that can disturb a representative multivariate signal response acquisition. Such effects rarely carry information that relates to the desired quantitative measurement. These effects may be caused by poor signal throughput, unstable radiation sources, unstable detector characteristics, random sporadic emissions, or various interfering background processes. It is common to reduce the impact of these effects on a subsequent calibration process by preprocessing the raw multivariate signal response. Useful preprocessing techniques include, for example: signal smoothing such as moving average filters and spline filters; double beam reference corrections such as the standardization method disclosed in U.S. Pat. No. 5,455,673; mean centering; differential derivative processing, i.e., computing a first or second derivative; spike filters; axis conversions, such as with spline functions; instrumental response compensations; and multiplicative signal correction estimation.
In their most useful applications, both NIRS and Raman spectrometry require the development of calibration models that correlate the acquired multivariate signal responses to quantitative measurements obtained by a reference technique. Correction and calibration of NIRS measurements is described in, for example, Geladi et al., "Linearization and Scatter-Correction for Near-Infrared Reflectance Spectra of Meat," Appl. Spec., 1985, Vol. 39, pp 491-500; Isaksson et al., "The Effect of Multiplicative Scatter Correction (MSC) and Linearity Improvement in NIR Spectroscopy," Appl. Spec., 1988, Vol. 42, pp. 1273-1284; Aastveit et al., "Near-Infrared Reflectance Spectroscopy: Different Strategies for Local Calibrations in Analysis of Forage Quality," Appl. Spec., 1993, Vol. 47, pp. 463-469; Isaksson et al., "Piece-Wise Multiplicative Scatter Correction Applied to Near-Infrared Diffuse Transmittance Data from Meat Products," Appl. Spec., 1993, Vol 47, pp 702-709; and Miller et al., "A Pathlength Correction Method for Near-Infrared Spectroscopy," Appl. Spec., 1990, Vol 44, pp. 895-898, the disclosures of which are incorporated herein by reference.
All NIRS and Raman spectra of light diffusing solids are affected by particle size and by the presence of liquids in the sample. For example, in liquid samples the amount of turbidity, particulates, and bubbles, or changes in the solution refraction index may change the strength of the observed signal. For solid samples, the sample shape, uniformity, and thickness may change the strength of the observed signal. For powdered or granulated samples, the particle size, shape and/or the packing density of the material may change the observed signal strength.
When samples do not change with time, or if the spectra of time-dependent samples are collected in a multiplexed fashion, i.e., the responses at all wavelengths are measured simultaneously, the impact of changes in observed signal strength is to multiply each spectrum by an unknown constant that is unique to that individually collected spectrum. Spectral responses that have been multiplied by an unknown random number are not suitable for calibration directly using the usual multivariate statistical approaches such as PCR or PLS. Several approaches to dealing with normalization problems have previously been proposed, for example, in Martens and Naes, Multivariate Calibration, John Wiley & Sons, New York, 1989, pp. 336-351, the disclosure of which is incorporated herein by reference. These approaches include normalization by closure, internal standards, and multiplicative scatter correction (MSC).
The normalization by closure method divides the original instrument responses at each point by the summation of all instrumental response points. This method is most useful when a relative instrumental response is adequate for the solution of the problem. However, in situations where the responses of the components vary greatly, the normalization by closure procedure can introduce artificial intercorrelations that makes it unsuitable for providing a spectral set in which the responses are proportional to the chemical compositions of the samples.
The use of an internal standard can be effective for solving some normalization problems. With this method, an additive having known response characteristics is introduced into the sample. The introduction of the additive provides a means to obtain a normalization constant by which the multivariate signal response can be corrected. While this method can be useful under some circumstances,it requires that an additive be introduced into the sample, which may not be practical in a production environment. Thus, the internal standard method does not provide a general solution to normalization problems.
The MSC method is based on the fact that the wavelength dependency of light scattering is different from that of chemically based light absorbance. Because of these dependencies, the data at many wavelengths can be used to distinguish, for example, between light absorption and light scattering. MSC may be suitable for analysis of an unknown sample containing several components, all of which have similar spectra, but it would not work well in situations where the spectral response represents several components varying over a wide composition range.
For the acquisition of quantitative measurements in production environments, one common approach to on-line monitoring is the continual removal from a stream of a small amount of material that is then processed through a "sampling system" to prepare it for the analysis. Commonly, the sampling system would condition the sample by, for example, removing bubbles, particulates, and turbidity; regulating temperature; or generally providing a constant observation condition. This would allow analytical apparatus such as a multivariate spectroscopy system to collect a spectrum that is reproducible to the extent necessary to relate to the constitution of the sample.
In favorable cases, the stream to be analyzed may have a spectral "signature" that enables the normalization of the spectral response. For example, one of the major components could have a distinct spectral response that does not interfere with the spectral response of other components in the sample. Under such limiting circumstances, variations in pathlength, turbidity or the like might be corrected by ratio methods to produce a robust calibration, but this approach would not be applicable to many industrial production situations.
It is also possible to estimate a calibration by using synthetic samples formulated in the laboratory to simulate what is thought to be in a process stream. However, practical experience indicates that it is usually better to calibrate the multivariate signal response in situ by measuring the multivariate signal response in the process and comparing it with quantitative measurements obtained from material samples removed from the manufacturing stream. In this situation, the spectra would contain all the variations of the real system of interest.